Law of the conservation of averages: The averages of population numbers of the two species remain constant and independent of the initial values of both populations if and only if the coefficients of growth and decay and the conditions of predation (prey losses, predator gains, i.e. Law of the periodical cycle: The fluctuations of two species populations, where one feeds on the other, are periodic, and the period depends entirely on the coefficients of growth ( r) and decay ( m) and initial conditions ( No and Po). Volterra (1928) summarized the properties of predator-prey interactions in three “laws” That in turn releases predation mortality from the minuscule prey populations, which will have great conditions and start growing exponentially – after which history repeats itself, the predator will increase, the prey collapse, the predator collapse. The slower-growing predators will survive for a while, but in a simple two species systems, they will eventually collapse as well.

Systems modelled with such assumptions are unstable, initially the predator population may grow if there are plenty of prey around, but as it grows, the prey population gets more impacted and at some point the prey will collapse. Which means that more predators ( P) leads to more predation, and more prey ( N) means more predation – the consumption is the product of the two and the search rate constant. If you examine these equations carefully, you’ll notice that the predator’s consumption ( Q) is calculated as Where g is the growth efficiency with which the predator converts consumption to production. Where the factor a is called the search rate. For the prey population, we describe the change over time with the differential equation, In a simple predator-prey system with no resource limitations for prey, the equations can be coupled. The basis is that with no resource limitations and no predators, prey populations ( N) will change over time with an exponential growth rate ( r),Īnd predator populations ( P) will decrease with a mortality rate ( m, due to e.g., starvation or old age), Models based on these sources are called Lotka-Volterra models and they are in essence the foundation for all predator-prey models, including the dynamic models in EwE.

The foundation for this was laid a century ago, when Lotka and Volterra both and independently formulated a theory for predator-prey interactions. If we are to successfully manage ecosystems, then species interactions is part of the equation. And yes, fish eat fish, and that has implications for management of living resources in aquatic environments. Andersen created one of the first end-to-end ecosystem models – often said. “ Fish eat fish“, Erik Ursin – who along with K.P. when we address questions at the ecosystem-level we have no choice. If the assessments are short-term, as single species assessments tend to be, we can get by assuming ‘business as usual’, but when we move away from the initial state, i.e. So is the case for species interactions as the quote above illustrates. Ray Beverton and Sidney Holt in their book set the vast part of the agenda that fisheries scientists have worked on ever since. This is a generalization of what is now perhaps the central problem of fisheries research: the investigation not merely of the reactions of particular populations to fishing, but also of interactions between them and the extent to which it is possible and practicable to derive laws describing the behavior of the community from those concerning the properties of component populations” “Elton (1949) has suggested that the goal of ecological survey is ‘…to discover the main dynamic relations between populations living in an area’. In their 1957 Magnus Opus, “On the Dynamics of Exploited Fish Populations” they wrote (p.24): Views on this question go back a long time as expressed by the two pioneers that more than any established fisheries science as a quantitative discipline, Ray Beverton and Sidney Holt. How do we manage this species in this bay this year? What we need to ask is, however, if it is sufficient? Let there be no doubt, single species assessment is a necessary factor for management of fisheries, notably for tactical management. 2 Modelling predator-prey interactions On the path to ecosystem-based management: species interactions

Predator vs prey model